The same restriction also applies to printer DCs.
Printer DCs must be created and destroyed on the same thread.
The printing team imposed this additional rule in order to make
it easier for printer driver vendors to author their drivers.
(Printer driver developers have a habit of calling
CoInitialize in their implementation of
CreateDC and
CoUninitialize in their implementation of
DeleteDC.)

Given that printer drivers are
a third-party extension point,
it's probably in your best interest to treat printer DCs
as having hard thread affinity,
since who knows what the printer driver is going to do
if you try to access it from multiple threads.
In other words,
the thread that creates the printer DC
should be the only thread which prints to it,
and should also be the thread which destroys the printer DC
when printing is complete.

That's not saying that all your printing has to be done
from one thread.
If you want,
you can create multiple printer DCs, each on different threads.
Just make sure to use each printer DC only on the thread
that created it.
Your printer driver will thank you.